In modern engineering systems, reliability and safety can be conferred by efficient automatic monitoring and fault detection algorithms, allowing for the early identification and isolation of incipient faults. In case of large-scale and complex systems, scalability issues and computational limitations make centralized monitoring and fault detection methods unapplicable. Research is therefore currently focusing on the development of distributed methods, where the computational complexity is divided among different units. In this paper, we propose a partition-based model-based fault detection and isolation scheme based on moving horizon estimation, able to estimate both the state variables and the possible faults, modeled as additive signals on the state and/or output equations. Its theoretical properties are analyzed, and numerical simulations are performed to witness its potentialities in a benchmark case study.